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arXiv · 1803.05373

Rigid reflections and Kac--Moody algebras

Kyu-Hwan Lee·Kyungyong Lee
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Abstract

Given any Coxeter group, we define rigid reflections and rigid roots using non-self-intersecting curves on a Riemann surface with labeled curves. When the Coxeter group arises from an acyclic quiver, they are related to the rigid representations of the quiver. For a family of rank 3 Coxeter groups, we show that there is a surjective map from the set of reduced positive roots of a rank 2 Kac--Moody algebra onto the set of rigid reflections. We conjecture that this map is bijective.

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BibTeXRIS

Kyu-Hwan Lee, Kyungyong Lee. 2018-03-14. Rigid reflections and Kac--Moody algebras. https://arxiv.org/abs/1803.05373

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